The senior class is collecting orders for graduation, So far, 54% have ordered their yearbook, 58% have ordered their gown and 15% have ordered their gown but not their yearbook. Find that probability that a randomly selected senior...
1. has ordered both a gown and a yearbook.
2. has ordered a yearbook or a gown.
3. has ordered neither a yearbook nor a gown.
4. has ordered a yearbook but not a gown.

the volume of the region contained in the cylinder x² + y² = 9, bounded above by the plane z = x and below by the xy-plane is 0.

Given: The cylinder is x² + y² = 9, bounded above by the plane z = x and below by the xy-planeWe know that, the cylinder is x² + y² = 9Which is (x/a)² + (y/b)² = 1Where a = 3 and b = 3The plane is z = xThe region is bounded below by the xy-plane Thus, the volume of the region can be found by integrating z = x with limits of x² + y² ≤ 9.So, V = ∭ dx dy dz where the limits are given by the cylinder and the plane.V = ∫∫∫ (x) dV ... (1)Now, converting the integral into cylindrical coordinates we have,∫∫∫ (x) dV = ∫θ = 0 to 2π ∫r = 0 to 3 ∫z = 0 to r cos θ (r cos θ) rdzdrdθ ... (2)x = r cos θ, y = r sin θ, and z = z.We know that the limits of x² + y² ≤ 9 in cylindrical coordinates are 0 ≤ θ ≤ 2π, 0 ≤ r ≤ 3, 0 ≤ z ≤ r cos θ.Using (2) in (1), we haveV = ∫θ = 0 to 2π ∫r = 0 to 3 ∫z = 0 to r cos θ (r cos θ) rdzdrdθ= ∫θ = 0 to 2π ∫r = 0 to 3 [r² cos θ / 2] dr dθ= ∫θ = 0 to 2π [ 9 cos θ / 2 ] dθ= 9 [ sin θ ]θ = 0 to 2π= 0Thus, the volume of the region contained in the cylinder x² + y² = 9, bounded above by the plane z = x and below by the xy-plane is 0.

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Answer:

-164

Step-by-step explanation:

Hope this helps!

Answer:

  10 meters

Step-by-step explanation:

You want the length of a 200 square meter tarp that has a width of 20 meters.

The area of a rectangle is given by ...

  A = LW

Filling in known values, we have ...

  200 m² = L · (20 m)

  L = (200 m²)/(20 m) = 10 m . . . . . . . divide by the coefficient of L

The tarp is 10 meters long.

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Answer: uh its just 3

the degree is the power of the exponent on the x term

Answer:

i might be 25

Step-by-step explanation:

Remove the greatest common factor.

Both have a multiple of 2 in them

Both have a multiple of x in them

Therefore, both have a multiple of 2x in them.

Factor 2x out.

2x(y^2 -5)

Use difference of squares to factor the second term.

(2x) (y-5) (y+5) is factored form.

Hope this helps :)

Answer:

2x (y+5) (y-5)

Step-by-step explanation:

2x (\(y^{2}\)-25)

2x (y+5) (y-5)

Answer:

1.17*10^14 km

Step-by-step explanation:

kindly find attached the image for your reference

Step one:

The diameter of Mars is approximately 6794 km

hence the radius is = 6794/2= 3397km

Step two:

Use the Pythagorean Theorem

\(x^2 + 3397^2 = (3397 + 25)^2\\\\\)

\(x^2 + 11539609 = (11710084)^2\\\\x^2 + 11539609 = (11710084)^2\\\\x^2= (11710084)^2-11539609 \\\\x^2= 1.37*10^14-11539609 \\\\x^2=1.37*10^14\\\\x= √1.37*10^14\\\\x=1.17*10^14 km\)

Answer:

9

Step-by-step explanation:

12 students could pick up a bag 3 times each.  This would account for 36 of the bags, leaving 9, with each recipient holding 3 bags.  9 bags is not enough so that each student would receive 1 more full bag.  

In conclusion, 9 students would receive 4 bags, but the remaining 3 students would receive fewer than 4 bags.

Answer:  9

Step-by-step explanation:

If they kept taking the bags, every student would get three. but then, 9 are left. it would be 36 r9, and our remainder is the answer.

Answer:

\(y=3x+3\)

Step-by-step explanation:

Use the slope-intercept form:

\(y=mx+b\)

m is the slope and b is the y-intercept. The y-intercept is the place where x is equal to 0, and the slope is the change in the y-axis over the change in the x-axis, otherwise known as rise over run ( \(\frac{rise}{run}\) ).

If you study the graph, you can see that the line crosses the y-axis at (0,3), so 3 is the y-intercept. Insert into the formula:

\(y=mx+3\)

Now find the slope. Use the slope formula:

\(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{rise}{run}\)

You need two points first. You can use the y-intercept (0,3) and another even point, like (1,6). Insert the values:

\((0_{x1},3_{y1})\\(1_{x2},6_{y2})\\\\\frac{6-3}{1-0}=\frac{3}{1}=3\)

The slope is 3. Insert this value:

\(y=3x+3\)

:Done

In the above case, the possible point system will be:

1st choice vote: 4 points

2nd choice vote: 2 points

In arranging for the turtle to win in this point framework, the point values relegated for 1st choice and 2nd choice votes have to be meet the taking after criteria:

Lets say:

1st choice vote: 4 points

2nd choice vote: 2 points

Thus by the use of these point values, the turtle would have the next chance of winning since 1st choice votes would be worth more point (4 point ) compared to 2nd choice votes (3 point ). This would push individuals to select the turtle as their 1st choice, because it would allow the turtle a better add up to point gains and increase its chances of winning.

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The conditional expectation E[Y|X=2] is 11, and the variance of Y, var(Y), is 24, given the linear relationship Y = 15 - 2X and a variance of 6 for X.

The conditional expectation E[Y|X=2] represents the expected value of Y when X takes on the value 2.

Given the linear relationship Y = 15 - 2X, we can substitute X = 2 into the equation to find Y:

Y = 15 - 2(2) = 15 - 4 = 11

Therefore, the conditional expectation E[ Y|X=2] is equal to 11.

To calculate the variance of Y, var(Y), we can use the property that if X and Y are linearly related, then var(Y) = b^2 * var(X), where b is the coefficient of X in the linear relationship.

In this case, b = -2, and the variance of X is given as 6.

var(Y) = (-2)^2 * 6 = 4 * 6 = 24

Therefore, the variance of Y, var(Y), is equal to 24.

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Answer:

0.07017

Step-by-step explanation:

The required interval of the given normal distribution using the empirical rule is [100, 140].

The empirical rule formula (also known as a 68 95 99 rule formula) uses data from a normal distribution to determine the first, second, and third standard deviations, which, respectively, differ from the mean value by 68%, 95%, and 99%. Additionally, it shows that 99.9% of the data fall inside the third standard deviation range (either above or below the mean value). The empirical rule formula is described below with cases that have been resolved.

In the question, we are given that IQ scores for adults aged 20 to 34 years are normally distributed according to N(120, 20), and are asked for the range in which the middle 68% of people in this group score on the test.

N(120, 20) signifies a normal distribution with mean, μ = 120, and the standard deviation, σ = 20.

By the empirical formula, 68% of the data lies within one standard deviation from the mean.

Thus, the required interval is [μ - σ, μ + σ] = [120 - 20, 120 + 20] = [100, 140].

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Answer:

Your answer is 15 which is your rate of change/slope

Step-by-step explanation:

To calculate rate of change/slope which also means the gradient we need any two points from the figure for the formula

\(m=\frac{y_2-y_1}{x_2-x_1}\)

I took the points (2,30) and (4,60)

so we put the values in our formula

\(m=\frac{60-30}{4-2}\)

\(m=\frac{30}{2} \\m=15\)

Answer:

9 7/10 is a decimal number is 9.7

The common ratio of the geometric sequence is 10.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed non-zero number called the common ratio. The general term. aₙ, of a geometric sequence is given by the formula

aₙ = a₁ r⁽ⁿ⁻¹⁾

where:

a₁ is the first term of the sequence

r is the common ratio

To find the common ratio of a geometric sequence, you can simply divide any term by the previous term in the sequence. In our case, the common ratio of the geometric sequence 0.1, 1, 10, 100 is:

1 / 0.1 = 10

10 / 1 = 10

100 / 10 = 10

Hence, the common ratio of the sequence is 10.

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Answer: (-1,7)

Step-by-step explanation:

If the function f(g(x)) = x passes through (7, -1). then the function g(f(x)) = x passes through (-1, 7).

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

The graph of function f passes through (7,-1). Function g satisfies f(g(x)) = x and g(f(x)) = x for all real numbers.

At x = -1, we have the function f

\(f(7) = -1\)

The function g is an inverse of function f.

\(g(-1) = 7\)

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2 is the constant of proportionality for the relationship given in the table.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

By using the formula y=kx we find this

k is the constant of proportionality.

0.8=k(0.4)

Divide both sides by 0.4

k=0.8/0.4

k=2

Hence, 2 is the constant of proportionality for the relationship given in the table.

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The value of $100 in euros is $87.

Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

Worth of 1 United States dollar is $0.87 in euros.

To find the value of $100 in Euros, use ratio property,

1 United States dollar = $0.87 in euros

100 United States dollar = $87 in euros.

The value of $100 in euros is $87.

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Answer:

de choices i see are matcheing up to A not sure tho could be C

Step-by-step explanation:

codeine

Part A: The total value of the loan with the simple interest is $58,290.75.

Part B: The total value of the loan with the quarterly compounded interest is $59,309.03.

Part C: The total value of the loan with the continuously compounded interest is  $59,440.06.

Part D: The best choice for the small business owner would be the loan with simple interest, as it has the lowest total value.

Part A: To determine the total value of the loan with simple interest, we can use the formula:

Total Value = Principal + (Principal * Interest Rate * Time)

Given:

Principal (loan amount) = $50,000

Interest Rate = 6.15% = 0.0615 (in decimal form)

Time = 3 years and 7 months = 3.58 years (approximated to two decimal places)

Total Value = $50,000 + ($50,000 * 0.0615 * 3.58)

Total Value ≈ $58,290.75

Part B: To determine the total value of the loan with quarterly compounded interest, we can use the formula:

Total Value = Principal * (1 + Interest Rate / Number of Compounding Periods)^(Number of Compounding Periods * Time)

Given:

Principal (loan amount) = $50,000

Interest Rate = 6.15% = 0.0615 (in decimal form)

Number of Compounding Periods = 4 (quarterly compounding)

Time = 3 years and 7 months = 3.58 years (approximated to two decimal places)

Total Value = $50,000 * (1 + 0.0615 / 4)^(4 * 3.58)

Total Value ≈ $59,309.03

Part C: To determine the total value of the loan with continuously compounded interest, we can use the formula:

Total Value = Principal * e^(Interest Rate * Time)

Given:

Principal (loan amount) = $50,000

Interest Rate = 6.15% = 0.0615 (in decimal form)

Time = 3 years and 7 months = 3.58 years (approximated to two decimal places)

(e is the mathematical constant approximately equal to 2.71828)

Total Value = $50,000 * e^(0.0615 * 3.58)

Total Value ≈ $59,440.06

Part D: Comparing the total values of the loan options:

- Total value with simple interest: $58,290.75

- Total value with quarterly compounded interest: $59,309.03

- Total value with continuously compounded interest: $59,440.06

Based on these values, the best choice for the small business owner would be the loan with simple interest, as it has the lowest total value. However, it's important to note that other factors such as repayment terms and flexibility should also be considered in addition to the total value.

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Answer: 5^6

Step-by-step explanation:

First, you have to simplify the numbers so that all of them share the same base. For this problem, the base for all of these numbers would be 5. So now the equation looks like this:

5^2 * 5^1 * 5^3

Next we have to turn all of these numbers into one. Whenever you multiply the numbers, all you have to do is add the exponents together. So now it will look like this:

5^(2+1+3)

Add the numbers up and you get your answer.

5^6

Answer:

Answer for 1

3. 21,356 x one half

Answer for 2

1. A and C

Step-by-step explanation:

Answer:

Step-by-step explanation:

The equation of a circle with center (h,k) and radius r is given by

(x-h)^2+(y-k)^2=r^2

Here given radius=3 and centre(h,k) is (0,2)

Therefore the equation of the required circle is,

(x-0)^2 + (y-2)^2 =3^2

x^2+y^2-4y-5=0

Now substituting for x and y

points (0,5)

0^2+5^2-4*5-5=0

So yes the points (0,5) lie on this circle

Answer:

32

Step-by-step explanation:

First you're going to change 20% to a decimal which would be 0.20

Next, multiply .20 by 40

You should get 8

Subtract 8 from 40

You're answer is 32

To find the probability of the event "the first die is 6 or the sum is 8," we need to count the number of outcomes that satisfy this event and divide it by the total number of possible outcomes.

To find the probability of the event "the first die is 6 or the sum is 8," we need to consider the total possible outcomes when rolling two dice and the favorable outcomes for this event.

Total possible outcomes: 6 sides on each die, so there are 6 x 6 = 36 possible outcomes.

Favorable outcomes:
1. First die is 6: There are 6 possible outcomes (6,1), (6,2), (6,3), (6,4), (6,5), and (6,6).
2. Sum is 8: There are 5 possible outcomes (2,6), (3,5), (4,4), (5,3), and (6,2).

However, (6,2) is counted twice, so we should subtract 1 from the total favorable outcomes: 6 + 5 - 1 = 10.

Probability = Favorable outcomes / Total possible outcomes = 10/36. Simplifying the fraction gives 5/18.

So, the probability of the event "the first die is 6 or the sum is 8" is 5/18.

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Answer:

(i) 1/2

(ii) 3/20

Step-by-step explanation:

(i) given total number of white counters = 10

total outcomes = 20 (3+10+5+2)

so it's 10/20

by simplifying it we get 1/2

(ii) given total number of red counters = 3

so it's 3/20

Answer:A I Believe

Step-by-step explanation:

Answer:

point-slope form, standard form, and slope-intercept form

Step-by-step explanation:

The three main types of linear functions are: point-slope form, standard form, and slope-intercept form.

Here is an image with each form

Answer:

No, they are not

Step-by-step explanation: